Advances in Civil Engineering

Volume 2018, Article ID 3410146, 12 pages

https://doi.org/10.1155/2018/3410146

## Probabilistic Prediction of Maximum Tensile Loads in Soil Nails

^{1}Assistant Professor, School of Civil Engineering, Guangzhou University, Guangzhou, Guangdong 510 006, China^{2}Postdoctoral Fellow, Department of Civil Engineering & Ryerson Institute of Infrastructure Innovation, Ryerson University, Toronto, ON, Canada M5B 2K3

Correspondence should be addressed to Peiyuan Lin; ac.nosreyr@nil.nauyiep

Received 21 August 2018; Revised 29 October 2018; Accepted 6 November 2018; Published 22 November 2018

Guest Editor: Haiyun Shi

Copyright © 2018 Yongqiang Hu and Peiyuan Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents the development of a simplified model for estimation of maximum nail loads during or at completion of construction of soil nail walls. The developed simplified nail load model consists of two multiplicative components: the theoretical nail load and the correction factor. The theoretical nail load is computed as the product of lateral active Earth pressure at nail depth and the nail tributary area. The correction factor is introduced to account for the difference between the theoretical and the measured nail loads. A total of 85 measured nail load data were collected from the literature; out of which, 74 were used to develop a simple formulation for the correction factor, whereas the remaining 11 were used for validation. After the validation, the model was updated using all 85 data. The updated simplified nail load model was demonstrated to be accurate on average (mean of model factor equal to 1), and the spread in prediction quantified as the coefficient of variation of the model factor was about 40%. Here, model factor is the ratio of measured to estimated nail load. The randomness of the model factor was also verified. Finally, the model factor was demonstrated to be a lognormal random variable. The proposed simplified nail load model is beneficial due to its simplicity and quantified model uncertainty; thus it is practically valuable to both direct reliability-based design and load and resistance factor design of soil nail wall internal limit states.

#### 1. Introduction

Estimation of maximum tensile loads for soil nails during or at completion of construction of soil nail walls is of great practical interests to wall design engineers. Due to the nail-soil interactions, tensile loads develop along soil nails as the nailed soil mass deforms. Failures due to nail pullout or yield in tension take place when the maximum tensile load in a nail exceeds its ultimate pullout capacity or yield tensile strength [1].

There have been several models proposed in the literature for estimation of maximum loads of soil nails during or at completion of wall construction. Juran and Elias [2] developed a modified apparent Earth pressure diagram model which was later found to be not practical as the estimated nail loads are very sensitive to input parameters such as soil friction angle and soil cohesion. Juran et al. [3] proposed a kinematical approach to compute nail loads as the wall construction proceeds and validated their approach using one case study. The underlying model uncertainty of the kinematical approach is not reported in the literature. The Federal Highway Administration (FHWA) soil nail wall design manuals [1, 4, 5] provide a simplified model for nail load estimation. Lin et al. [6] evaluated the model uncertainty of the FHWA simplified model using 45 measured maximum nail load data they collected from the literature and concluded that the default FHWA simplified nail load equation is excessively conservative on average and the estimation scatters widely. Moreover, the model factor of the FHWA equation is not a random variable as it is statistically correlated to some of the input parameters and the calculated nail load. Here, model factor is the ratio of measured to calculated nail load. They then modified the FHWA simplified nail load model to improve on-average accuracy, reduce spreads in prediction accuracy, and remove the dependency between model factor and input parameters and calculated nail load. Indeed, the dependency issue has been reported for various geotechnical models, e.g., bearing capacity of foundations [7–9], both pullout capacities and tensile loads of reinforcing elements in reinforced soil walls [6, 10–13], and deflection of cantilever walls [14]. Removal of this type of dependency is important for geotechnical reliability-based design as emphasized in ISO2394:2015 Annex D [15] and Phoon [16]. Influence of the dependency on reliability analysis outcomes was discussed by Lin and Bathurst [17].

In this study, a total of 85 measured data for maximum nail tensile loads during or at completion of wall construction are first collected from the literature and divided into two data groups. The first data group is used to develop a simplified model for nail load estimation based on the two regression approaches introduced in Dithinde et al. [18]. The developed simplified model is then validated using the other data group. The simplified model proposed by the present study is advantageous when compared to the default and modified FHWA simplified nail load models from the perspectives of number of empirical constants (i.e., two versus three and five), on-average accuracy (i.e., accurate versus conservative), spread in prediction accuracy (i.e., about 40% versus about 45% and 50%), and dependency between model factor and input parameters or computed nail load. Finally, the distribution of the model factor of the proposed equation is also discussed.

#### 2. Formulation of Simplified Model for Calculation of Maximum Nail Loads

A soil nail wall system is typically divided into an active zone and a passive zone by a potential slip surface, as shown in Figure 1. Nails are installed immediately after excavation of each level to provide both pullout resistance against global failure and restraint against lateral deformation of the excavated ground. Tensile loads are then developed along nails mainly due to the frictional interaction between nails and the surrounding soil and the soil-structure interaction between the facing and the soil at nail heads [19]. The lateral Earth pressure acting within a tributary area where a soil nail center is carried by that nail. Based on this mechanism, the tensile load in a soil nail can be calculated as follows:where is the theoretical nail load computed as is the horizontal Earth pressure at depth of nail head as defined in Figure 1; is the active Earth pressure coefficient computed using Coulomb theory; is the soil unit weight; is the surcharge load; and are the horizontal and vertical nail spacing, respectively; and is the empirical correction factor introduced to account for errors arising from underlying model errors, variability in soil properties, and all types of uncertainties in sites, etc. The Coulomb is computed as follows:where = face batter angle; = effective soil friction angle; = back slope angle; and = interface friction angle between the wall face and soil.